Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.

Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter

我们为核子数量介子系统，一个任意的吝啬的分级的介子领域在被介绍建议一个量子化过程。有平常的这个过程的等价为任何给定的价值被证明。由这个过程的使用，在 Walecka 的 MFA 并且在下巴的 RHA 的分级的介子领域在保持的平均数附近被使量子化。它这些理论上的修正被不安考虑直到第二份订单。任意使我们自由在计算在任何阶段修理它。当我们以 Walecka 的 MFA 的方法修理它时，量修正大，并且结果不收敛。当我们以下巴的 RHA 的方法修理它时，量修正是微不足道的小的，并且集中是优秀的。它证明 RHA 为原子系统盖住量地理论的领先的部分并且是为进一步的量修正的优秀 zeroth 顺序近似，当 Walecka 的 MFA 不做时。我们建议由为有限原子核为原子事或全部的精力最小化全部的精力每核子在整个计算的目的修理参数，到使使量子化的相对论的吝啬的地理论(QRMFT ) 成为一个变化方法。

Fast impurity solver for dynamical mean field theory based on second order perturbation around the atomic limit

This paper proposes an impurity solver for the dynamical mean field theory （DMFT） study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA （local density approximation） ＋ DMFT studies of the Mort insulators with long range order.

Investigations on Nuclei near Z = 82 in Relativistic Mean Field Theory with FSUGold

In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field （RMF） theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.

Exotic Structures of Odd-A Carbon Isotopes in the Deformed Relativistic Mean-FieldTheory

We study contributions of the pion meson and spatial component of the omega meson in the odd-A carbonisotopes. The pion and spatial omega provide small attractions in odd-A nuclei, giving rise to considerable influences onthe single-particle energies rather than the bulk properties such as total binding energies, and root-mean-square (rms)radii. The ±Ω (spin) splittings, arising from the spatial omega, are large in ^1^1C and ^1^3C and drop as the isospin rises inodd-A carbon isotopes. As an isovector, the pion can shift slightly the relative potential depth of neutron and proton,contrary to the role of the rho meson. There is a general trend that both the pion and spatial omega fields reduce withthe rise of isospin in the isotopic chain. From the normal nucleus to halo nucleus, an abnormal drop of the pion or spatialomega field may occur, as can be seen in ^1^9C, ^1^5C, and ^2^1C.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

octupole 变丑和弄平甚至 Rn， Th 和 U 同位素的另外的扎根的州的性质在思考的框架以内系统地被调查不对称的相对论的吝啬的地(RAS-RMF ) 模型。计算结果复制有约束力的精力和四极变丑很好。计算结果在状态演变从的地面显示这些原子核将近球形(N = 130 ) 形状到有中子数字的增加的四极变丑形状。在 Rn 同位素之中，仅仅 222,224Rn 是使变形的 octupole，为他们的 octupole 变丑是小的，这也被发现。然而，在 Th 和 U 同位素的更多的原子核(N 134148 ) 是使变形的 octupole，为他们中的一些的 octupole 变丑是重要的(| 3 |~ 0.1 或甚至更大) 。

Shape Coexistence for ^179Hg in Relativistic Mean-Field Theory

The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.

Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure

运输网络例如铁路网络和机场网络，是有复杂拓扑学的一种随机的网络。最近，越来越多的学者注意了运输网络和尝试的各种各样的类型探索他们的固有的特征。这里，我们与随机的重叠派系结构学习一个最近介绍的公共汽车运输网络(BTN ) 进化模型的指数的性质，它在中国为三个主要城市的一些 BTN 的连接的观察指数的分发给可能的解释。适用的吝啬地的理论，我们分析 BTN 模型并且证明这个模型有连接的指数的分发的特性，并且开发一个方法预言单个顶点的生长动力学，并且使用这计算经分解连接分发和代表。由把吝啬地的基于的理论上的结果与真实 BTN 的统计数据作比较，总体上，我们他们的数据表演观察那连接的指数的分发的类似的特性，和他们的代表有一样的数量级，它显示出这份报纸的分析结果的可获得性。

Resonant Continuum in the Relativistic Mean－Field Theory

Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.

Kinetic Ising model in a time-dependent oscillating external magnetic field:effective-field theory

Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory （EFT） and a mean-field theory （MFT）. The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency （w） and static external field amplitude （h0） for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

混合 spin-3/2 和混合 spin-3/2 和 spin-5/2 Ising 的磁性有不同 anisotropies 的铁磁性的系统借助于吝啬地的理论(MFT ) 被学习。单个离子的 anisotropy 力量上的阶段图的依赖也被学习。在混合 spin-3/2 和 spin-2 Ising 模型，除秒顺序阶段转变以外，第一顺序混乱阶段转变和 tricritical 线被发现。在混合 spin-3/2 和 spin-5/2 Ising 模型，没有一阶的转变和 tricritical 线。

一种新的k-means聚类雷达信号分选算法

针对传统k-means聚类算法在雷达信号分选中应用存在的不足,提出了一种基于数据场和灰关联分析的k-means聚类雷达信号分选算法。该算法首先根据数据场理论计算所有数据样本的势值,寻找局域势值最大值,选取距最大值最近的样本数据作为初始聚类中心,局域势值最大值个数作为聚类数目;然后用灰关联度代替欧式距离来判断数据样本间相似性。该算法能够自动获取初始聚类中心和聚类数目,对频率捷变雷达具有较好的分选效果。仿真结果验证了算法的可行性。

深度神经网络平均场理论综述

平均场理论(MFT)为理解深度神经网络(DNN)的运行机制提供了非常深刻的见解,可以从理论上指导深度学习的工程设计。近年来,越来越多的研究人员开始投入DNN的理论研究,特别是基于MFT的一系列工作引起人们的广泛关注。为此,对深度神经网络平均场理论相关的研究内容进行综述,主要从初始化、训练过程和泛化性能这三个基本方面介绍最新的理论研究成果。在此基础上,介绍了混沌边缘和动力等距初始化的相关概念、相关特性和具体应用,分析了过参数网络以及相关等价网络的训练特性,并对不同网络架构的泛化性能进行理论分析,体现了平均场理论是理解深度神经网络机理的非常重要的基本理论方法。最后,总结了深度神经网络中初始、训练和泛化阶段的平均场理论面临的主要挑战和未来研究方向。

二维各向异性海森伯反铁磁性的Schwinger-Boson平均场解法

运用共振价键概念和Schwinger-Boson平均场近似,研究了二维正方格子上的各向异性Heisenberg反铁磁性。结果表明,耦合率α=J_y/J_x达到临界值α_0时,系统发生有序一无序相变;α>α_0时,温度超过T_N(Nèel温度),发生有序一无序相变;α<α_0时,系统存在能隙,各向同性的一维和二维系统具有共同的失耦温度T_D。当温度接近T_D时,共振价键序参量迅速减为零。

Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory （ITP） of the dynamical mean field theory （DMFT） and coherentpotential approximation （CPA） is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tij^mn（m ≠ n） are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.

Dyson–Maleev theory of an X X Z ferrimagnetic spin chain with single-ion anisotropy

We use the mean-field approximation of Dyson–Maleev representation to study an XXZ Heisenberg ferrimagnetic spin chain with single-ion anisotropy. By solving the self-consistent equations with different anisotropies, λ and D respectively,the energy spectrums, internal energy, static susceptibility and specific heat are calculated. Especially, the quantum phase transition of the magnetization plateau induced by single-ion anisotropy D is obtained in the model of the ferrimagnetic spin chain by using Dyson–Maleev mean-field theory.

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random field （hi） is assumed to be Gaussian distributed with zero mean and a variance （hi2） = HRF2. The free energy （F）, the magnetization （M） and the order parameter （q） are calculated. The ferromagnetic （FM） spin-glass （SG） phase transition is clearly observed. The critical temperature （Tc） is computed under a critical intensity of random field HRF = V/2/πJ. The phase transition from FM to paramagnetic （PM） occurs at TC = J/k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility （X） shows a sharp cusp at TC and the specific heat （C） has a singularity in small random field. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulation.